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Full text of "Text Book Of Mechanical Engineering"

Continuous Beams.

445

OF REACTIONS ON SUPPORTS FOR CONTINUOUS BEAMS, AS FOUND
FROM CLAPEYRON'S THEOREM OF THREE MOMENTS' IN TERMS OF Wj
" UNIFORM LOAD ON EACH SPAN.

2 Spans 3 Spans 4 Spans 5 'Spans 6 Spans 7 Spans 8 Spans 9 Spans
	
	
	
	
	(See
	also
	Appendices L and 7.L pp. 762 and 849.)
	
	i
 3 8
	1
 IO
 T
	I
 3 8
					
	10
	i
 ii
 IO
	1
 ii
 10
	1
 10
				
	1
 ii
 28
	1
 32 28
	26 28
	1
 32 28
	i
 ii
 28
			
	1
 IS 38
	1
 43 38
	I
 37 38
	1
 37 38
	i
 43 38
	l
 15
 38
		
	1 104
	118
 104
	1
 108
 104
	1
 106
 104
	1
 108
 104
	118
 104
	l
 JLL
 104
	

	1
 142
	161 142
	137 142
	_
	143 142
	37 142
	161 142
	142

	152
 388
	I
 440
 388
	374 388
	1
 392 388
	1
 386 388
	1
 392
 388
	1
 374 388
	1  I
 440 152 388 388

	209 530
	I
 601
 530
	1
 51* 530
	1
 535 530
	I
 529 530
	1
 529
 530
	1
 535 530
	1   1   1
 511 601 209
 530 530 530

Culmann's Funicular Polygon (Fig. 404) is a ready means
solving such a problem as (4) Fig. 402. Culmann of Zurich
proved that the bending moments are there proportional to the
:>:txlinates of a polygon obtained by hanging the same weights to a
uoose string hooked at the supports. Taking the loads in Fig. 404,
B o is drawn to scale, and represents the weights taken in order
shewn. Mark a point E any distance x ft. from c B, and join to
CL, M, N, and B. Draw from any point F, F o || c B, G H || M E, H j ||
EST 3E, and J K || B E. Join K F, and draw E L |j K F. The shaded
polygon is the curve of Bending Moment^ and

BM  vertical ordinate in Ibs. x x? (lb. ft.)